IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v33y2020i1d10.1007_s10959-019-00879-z.html
   My bibliography  Save this article

Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination

Author

Listed:
  • Chang-Song Deng

    (Wuhan University)

Abstract

In this paper, we are concerned with the subgeometric rate of convergence of a Markov chain with discrete-time parameter to its invariant measure in the f-norm. We clarify how three typical subgeometric rates of convergence are inherited under a discrete-time version of Bochner’s subordination. The crucial point is to establish the corresponding moment estimates for discrete-time subordinators under some reasonable conditions on the underlying Bernstein function.

Suggested Citation

  • Chang-Song Deng, 2020. "Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination," Journal of Theoretical Probability, Springer, vol. 33(1), pages 522-532, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-019-00879-z
    DOI: 10.1007/s10959-019-00879-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-019-00879-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-019-00879-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexander Bendikov & Wojciech Cygan, 2015. "On massive sets for subordinated random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 288(8-9), pages 841-853, June.
    2. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    3. Bendikov, Alexander & Cygan, Wojciech & Trojan, Bartosz, 2017. "Limit theorems for random walks," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3268-3290.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wojciech Cygan & Stjepan Šebek, 2021. "Transition probability estimates for subordinate random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 518-558, March.
    2. Fageot, Julien & Fallah, Alireza & Unser, Michael, 2017. "Multidimensional Lévy white noise in weighted Besov spaces," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1599-1621.
    3. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).
    4. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    5. Kühn, Franziska & Schilling, René L., 2019. "Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2654-2680.
    6. Iosif Pinelis, 2018. "Positive-part moments via characteristic functions, and more general expressions," Journal of Theoretical Probability, Springer, vol. 31(1), pages 527-555, March.
    7. Robin Merkle & Andrea Barth, 2023. "On Properties and Applications of Gaussian Subordinated Lévy Fields," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-33, June.
    8. Kühn, Franziska, 2017. "Existence and estimates of moments for Lévy-type processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 1018-1041.
    9. Julien Fageot & Michael Unser, 2019. "Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Lévy White Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1166-1189, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-019-00879-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.